Question

The point of contact of the line $y=x-1$ with $3x-4y^2=12$ is

• A. $(4,3)$
• B. $(3,4)$
• C. $(4,-3)$
• D. None of these

Answer 1

Answer: (A)

The equations of the line and hyperbola are
$y=x-1$ ... (i) $3x^2-4y^2=12$ ... (ii)
From Eqs. (i) and (ii), we get
$3x^2-4{(x-1)}^2=12$
$\Rightarrow$ $3x^2-4(x^2-2x+1)=12$
or $x^2-8x+16=0\Rightarrow x=4$
From Eq. (i), $y=3$
Hence, required point of contact is $(4,3)$ .